Accurate and Low-cost Indoor Location Estimation Using Kernels Jeffrey J. Pan, James T. Kwok, Qiang Yang, Yiqiang Chen Department of Computer Science Hong Kong University of Science and Technology Present in the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI-05), 1 Edinburgh, Scotland, July 2005.
Application Background HKUST � Positioning Outdoor : Road Guiding (GPS) � Indoor : Large Building (WiFi) � � Location-based Service Web Content Delivery � � Behavior Analysis Daily Life (L. Liao et al. AAAI-04, IJCAI-05) � Health Care � Scientific Purpose � 2
Problem Description HKUST A user with a mobile device walks in an indoor � wireless environment (Covered by WiFi signals) AP3 AP2 Time t: (-47dB,-36dB,-62dB) AP1 Where am I ? 3 Off-the-Shelf Hardware, Only Signal Strength
HKUST Radio 4 Map Noisy Propagation Channel at 2.4G AP2 Signal Obstructed Signal Obstructed AP1 AP3
Learning-based Location Estimation HKUST Two phases: offline Training and online Localization � Offline phase – collect samples to build a mapping function F � from signal space S to location space L Loc. Time (AP1,AP2,AP3) Training… (1,0) 1s (-60,-50,-40) dB Mapping function F (2,0) 2s (-62,-48,-35) dB ….. …. ( … , … , … )dB (9,5) 9s (-50,-35,-42) dB Online phase – given a new signal s , estimate the most likely � location l from F s = (-60,-49,-36)dB , compute F(s) as the estimated location � 5
Outline HKUST Introduction to Location Estimation � Application Background � Problem Description � Noisy Characteristics of Propagation Channel � Basic Framework for Location Estimation � Related Work � Microsoft Research’s RADAR (INFOCOM’2000) � University of Maryland’s Horus (PerCom’2003) � Motivation of Our Approach � The LE-KCCA Algorithm � Kernel Canonical Correlation Analysis (KCCA) � Choices of Kernels � Experimental Setup and Result � Strength and Weakness � 6 Future Work �
Related Works HKUST Microsoft Research’s RADAR [P. Bahl et al. INFOCOM2000] � K-Nearest-Neighbor Method � Offline - for each location, compute the signal mean � Online – estimate location with KNN and triangulation � � Strength Small number of samples could estimate the signal mean well � � Weakness Accuracy is relatively low � Reason – The K nearest neighbors retrieved in the signal space may � not necessarily the K nearest neighbors in the location space 7
Related Works (Cont’) HKUST University of Maryland’s Horus [M. Youssef et al. ,2003] � Maximum Likelihood Estimation (MLE) � Offline - for each location, build the Radio Map of each AP � Online - apply Bayes’ rule for estimation � Strength � Accuracy is high � Weakness � Need relatively large number of samples � Reason – More samples are needed for establishing an accurate � Radio Map rather than a signal mean Radio Map 8
Motivation of Our Approach HKUST � Observation (Motivated by RADAR) � Similar signals may not be nearby locations � Dissimilar signals may not be far away � Idea � Maximize the similarity correlation between signal and location spaces under feature transformation � Goal � Accuracy as high as possible ( Horus ) � Calibration Effort as low as possible ( RADAR ) 9
Motivation of Our Approach (Cont’) HKUST Original Original Signal Location Space Space Feature Feature Location Signal Space Space 10
(Kernel) CCA HKUST K ernel CCA � C anonical C orrelation A nalysis (CCA) � [H. Hotelling, 1936] [D.R Hardoon, S. Szedmak, and J. � � Two data set X and Y Shawe-Taylor, 2004] � Two linear Canonical Vectors Wx Wy � Two non-linear Canonical Vectors � Maximize the correlation of projections � K is the kernel � 11
LE-KCCA HKUST � Offline phase Signal strengths are collected at various grid locations. � KCCA is used to learn the mapping between signal and location spaces. � λ i ’s and α i ’s are obtained from the generalized eigen-problem � κ is a regularization term � For each training pair ( s i , l i ), its projections � on the T canonical vectors are obtained from 12
LE-KCCA (Cont’) HKUST Online phase � Assume the location of a new signal strength vector is s � Again, use � to project s onto the canonical vectors and obtain Find the K Nearest N eighbors of P ( s ) in the projections of training � set with the weighted Euclidean distance : Interpolate these neighbors’ locations to predict the location of s � Essentially, we are performing Weighted KNN in the feature space with � which weights are obtained from the feedback of location information. 13
Choices of Kernels HKUST Kernel for Signal Space � Gaussian Kernel to smooth the noisy characteristics � Widely used : [Roos et al. 2002, Battiti et al. 2002] � Kernel for Location Space � Matern Kernel to sense the change in location � Used in : GPPS [Schwaighofer et al., 2003] � 14
Experimental Setup HKUST Test-bed : Department of Computer Science, Hong � Kong University of Science and Technology � 99 locations (1.5 × 1.5 meter) � 100 samples per location 42m � 65% for training, 35% testing � Repeat each experiment 10 times 15 65m
Experimental Result - 1 HKUST � Accuracy Data Set � 65% training � 35% testing � Error Distance is 3.0m � LE-KCCA 91.6% � SVM 87.8% � MLE 86.1% � RADAR 78.8% � 16
Experimental Result - 2 HKUST � Reduce Calibration Effort Incrementally Use a small subset of the the 65% training data � Outperform the others using 10-15 samples from each location � 17
Recall our Motivation……… HKUST Original Original Signal Location Space Space Feature Feature Location Signal Space Space We could see on the next page…… 18
Visualization of Tracking in Both Original and Feature Spaces HKUST 70 40 Hallway 1 Hallway 3 35 60 Original Original 30 Hallway 2 50 Signal Location AP2 (unit:−dB) Y (unit:1.5m) 25 Hallway 2 Space Space 40 20 Hallway 3 15 30 10 20 Hallway 1 5 10 0 10 20 30 40 50 60 70 10 20 30 40 50 AP1 (unit:−dB) X (unit:1.5m) 15 15 10 10 Hallway 3 Hallway 3 Feature Feature Hallway 1 Hallway 1 5 5 Location Signal 0 Feature 2 Feature 2 0 Space Space −5 −5 −10 −10 −15 −15 19 Hallway 2 Hallway 2 −20 −20 −15 −10 −5 0 5 10 15 20 25 −15 −10 −5 0 5 10 15 20 25 Feature 1 Feature 1
Strength and Weakness HKUST � Strength � Higher Accuracy � Reduced Calibration Effort (Low-cost) � Weakness � Generally 50-100 times slower than RADAR 20
Future Work HKUST Consider Environment Dynamics to Reduce Uncertainty � J. Yin et al. Adaptive temporal radio maps for indoor location � estimation. PerCom’05 Consider User Dynamics to Reduce Uncertainty � M. Berna et al. A Learning Algorithm for Localizing People Based On � Wireless Signal Strength That Uses Labeled and Unlabeled Data. IJCAI’03 A. Ladd et al. Robotics-based location sensing using wireless ethernet, � MobiCom’02 Speed up for Large-Scale Localization � J. Letchner et al. Large Scale Localization from Wireless Signal � Strength. AAAI’05 A. Haeberlen et al. Practical Robust Localization over Large-Scale � 802.11 Wireless Networks. MobiCom’04 21
Acknowledge HKUST � Hong Kong RGC � HKUST6187/04E � Thanks Jie Yin and Xiaoyong Chai � Data collection � Helpful discussion 22
HKUST Thank You Question ? 23
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